Conventional pillow shells for bed pillows are most commonly made from only two rectangular sheets of fabric that are sewn together around three edges, inverted, filled with polyester or other suitable material such as down or foam, and then the final seam is sewn with whip stitching or serged. The result is a single four seam bed pillow. The sizes of these rectangular bed pillows range from standard 20×26 inches to jumbo at 20×28 inches, queen 20×30 inches, king at 20×36 inches and body at 20×54 or 20×60 inches. Many factors are significant when designing a bed pillow shell. On the one hand, it is desirable to create pillow shells that produce a distinctive visual appearance while easily accepting the necessary fill material, but on the other hand, it is necessary that the cost of manufacture be very nearly the same as the cost of the simple four seam rectangular pillow design. Numerous attempts have been made to create different appearances both for manufacturing efficiencies such as in U.S. Publication 2009/0106904 where a pillow is provided with rounded corners for ease of uniform filling, to U.S. Pat. No. 6,760,935 where a pillow is provided with four side gusset panels, and to U.S. Design Patent D507,960 where a pillow is provided with two oval side gusset panels and decorative piping. All of these previous designs suffer from various shortcomings including the complications of sewing curved seams, the material wasted when cloth is cut in curved segments, the numbers of seams required to be sewn, and the lack of adaptability to produce a variety of visual appearances. It would be desirable to have a new pillow shell configuration that could be easily manufactured with a limited number of straight seams and no wasted cloth due to using curved fabric pieces in the patterns.